The Comonad.Reader

Last time we derived an entailment relation for constraints, now let's get some use out of it.

Reflecting Classes and Instances

Most of the implications we use on a day to day basis come from our class and instance declarations, but last time we only really dealt with constraint products.

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Max Bolingbroke has done a wonderful job on adding Constraint kinds to GHC.

Constraint Kinds adds a new kind Constraint, such that Eq :: * -> Constraint, Monad :: (* -> *) -> Constraint, but since it is a kind, we can make type families for constraints, and even parameterize constraints on constraints.

So, let's play with them and see what we can come up with!

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Last time, I showed that we can build a small parsec clone with packrat support.

This time I intend to implement packrat directly on top of Parsec 3.

One of the main topics of discussion when it comes to packrat parsing since Bryan Ford's initial release of Pappy has been the fact that in general you shouldn't use packrat to memoize every rule, and that instead you should apply Amdahl's law to look for the cases where the lookup time is paid back in terms of repetitive evaluation, computation time and the hit rate. This is great news for us, since, we only want to memoize a handful of expensive combinators.

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You never heard of the Millenium Falcon? It's the ship that made the Kessel Run in 12 parsecs.

I've been working on a parser combinator library called trifecta, and so I decided I'd share some thoughts on parsing.

Packrat parsing (as provided by frisby, pappy, rats! and the Scala parsing combinators) and more traditional recursive descent parsers (like Parsec) are often held up as somehow different.

Today I'll show that you can add monadic parsing to a packrat parser, sacrificing asymptotic guarantees in exchange for the convenient context sensitivity, and conversely how you can easily add packrat parsing to a traditional monadic parser combinator library.

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Last night, Chung-Chieh Shan posted an example of a pointed-set monad on his blog, which happens to be isomorphic to a non-empty stream monad with a different emphasis.

But, I thought I should point out that the pointed set that he posted also has a comonadic structure, which may be exploited since it is just a variation on the "zipper comonad," a structure that is perhaps more correctly called a "pointing comonad."

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To those that have asked, I'm still alive.

I had to restore the blog database from a backup and so I lost a few posts, including the index for the various recursion schemes entries. Fortunately, before that happened I had replicated the catamorphism post as a knol.

Should I find myself with a copious glut of free time, I shall happily re-scribe and finish the rest, but I've been very busy.

Does anyone know of any work on "forgetful laziness?"

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Back in the days of HYLO, it was common to write hylomorphisms with an additional natural transformation in them. Well, I was still coding in evil imperative languages back then, but I have it on reliable, er.. well supposition, that this is probably the case, or at least that they liked to do it back in the HYLO papers anyways.

Transcoding the category theory mumbo-jumbo into Haskell, so I can have a larger audience, we get the following 'frat combinator' -- you can blame Jules Bean from #haskell for that.

 
hyloEta :: Functor f =>
     (g b -> b) ->
     (forall a. f a -> g a) ->
     (a -> f a)
hyloEta phi eta psi = phi . eta . fmap (hyloEta phi eta psi) . psi
 

We placed eta in the middle of the argument list because it is evocative of the fact that it occurs between phi and psi, and because that seems to be where everyone else puts it.

Now, clearly, we could roll eta into phi and get the more traditional hylo where f = g. Less obviously we could roll it into psi because it is a natural transformation and so the following diagram commutes:

This 'Hylo Shift' property (mentioned in that same paper) allows us to move the 'eta' term into the phi term or into the psi term as we see fit. Since we can move the eta term around and it adds no value to the combinator, it quietly returned to the void from whence it came. hyloEta offers us no more power than hylo, so out it goes.

So, if its dead, why talk about it?

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Wordpress changed the slug of this post, but Planet Haskell has the old link.

Here is the actual content.

Updated my little type-level 2s and 16s complement integer library to be ghc 6.6 friendly and uploaded it to hackage based on popular (er.. ok, well, singular) demand.

O.K. it was more of a polite request, but I did update it.